They must apply for Entry Clearance in the HSMP dependent visa category at the relevant British Dipomatic Post in their country of nationality or legal long term residence. Such requires the submission of Form VAF2 with applicable fees and supporting documents to include originals of:
1. Marriage certificate.
2. Child's full birth certificate with both parents names.
3. Child's passport.
4. Mother's passport.
5. Certified copies of your passport - bio data page and HSMP FLR residence permit page.
6. Evidence of funds - six month bank statement and payslips (12 months better).
7. Employer letter detailing position, term (permanen/ contract), length of service, salary.
8. Evidence of accomodation - tenancy agreement, mortgage statements
where rented consent of landlord for them to live there.
9. Letter (from estate agent/ local authority) with details of accomodation size to ensure there is no overcrowding.
10. In all cases utility bills (not mobile phone) as evidence of your tenancy/ residency
refer to
www.ukvisas.gov.uk for more info.
good luck